Question

In the given figure, if $x+y=w+z,$ then prove that $AOB$ is a line.

Answer 1

Let $x+y=w+z=a$

Complete angle at point $O$ $={360}^{\circ }$

$\angle BOC+\angle COA+\angle AOD+\angle DOB={360}^{\circ }$

$x+y+w+z={360}^{\circ }$

$a+a=360^{\circ }$

$2a=360^{\circ }$

$a=\frac{360^{\circ }}{2}=180^{\circ }$

$\Rightarrow x+y=180^{\circ }$

$\Rightarrow \angle AOB=180^{\circ }$

which is a supplementary angle

Hence proved that $AOB$ is line.